Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Partial null-controllabiliy of evolution equations by one-dimensional control

Benzion Shklyar

Abstract

The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution systems have been obtained using the moment problem approach.

Partial null-controllabiliy of evolution equations by one-dimensional control

Abstract

The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution systems have been obtained using the moment problem approach.
Paper Structure (15 sections, 14 theorems, 143 equations)

This paper contains 15 sections, 14 theorems, 143 equations.

Table of Contents

  1. Introduction and problem statement
  2. Coupled evolution systems
  3. The case $\mathchar"011B _{YZ}=\varnothing$
  4. Eigenvectors and eigenvalues
  5. Eigenvectors of operator $A$
  6. Eigenvectors of adjoint operator $A^{\ast }$
  7. Partial controllability conditions
  8. The case $b\in Y$
  9. One sufficient condition for strong minimality
  10. Example 1
  11. The case $\mathchar"011B _{YZ}\neq \varnothing$
  12. Eigenvectors of the operators $A$ and $A^{\ast }$
  13. Partial controllability conditions
  14. Example 2
  15. Conclusion

Key Result

Lemma 1

The sequences $\left\{ \mathchar"0127 _{Yj},j\in I_{Y}\right\}$ and $\left\{ \mathchar"0120 _{Yj},j\in I_{Y}\right\}$ are Riesz basics of the space $Y.$ The sequences $\left\{ \mathchar"0127 _{Zk},k\in I_{Z}\right\}$ and $\left\{ \mathchar"0120 _{Zk},k\in I_{Z}\right\}$ are Riesz

Theorems & Definitions (30)

  • Definition 1
  • Definition 2
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Definition 3
  • Theorem 2
  • proof
  • Remark 3
  • ...and 20 more